A “reaction function” estimation

Since the LM and RLM tests for spatial lag dependence signi…cantly indicate that communal tax multipliers are spatially correlated, we estimated a “reaction function” as given by equation (4.4). Taking for simplicity a linear approximation, the speci…cation to estimate can be written as:

t_j =P

k6=j

w_jkt_k+⁰_PX_jP +⁰_GX_jG+⁰ _GX _jG+"_j (4.6)

2 1To compute these tests, we used a15km weight matrix as described in appendix II. See Anselin et al.

(1996) for a description of these tests.

2 2The type of spatial error dependence we tested can be written as follows: "j =P

k6=j

wjk"k+uj where wjkis a weight coe¢cient and uj is aniiderror term.

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wherew_jk represents the weight assigned to the “neighbor” commune k and "_j is an error term. Given the large number of weights w_jk - 73⁰536 - to determine, it is not possible to estimate them along with the other parameters of equation (4.6). This implies that we must assume them to be known and therefore specify them a priori. Supposing that …scally induced migration occurs mostly at a very local level and that communes have larger social ties with communes nearby, we consider geographical distance between communes as a good proxy for neighborliness. For all the estimations reported in this paper, a15 km threshold is used.²³ The construction of the weights is described in appendix II.

The main econometric concern when estimating equation (4.6) is that the neighbor tax multipliers are endogenous. The reason is that all the communal tax multipliers are simultaneously determined in exactly the same fashion. As a result, the OLS estimates of the parameters of equation (4.6) may be a¤ected by a simultaneity bias. This endogeneity can be addressed by using either an instrumental variable (2SLS) approach or a maximum likelihood (ML) method. For our estimations, we rely on the 2SLS technique as used, for instance, by Besley and Case (1995), Brett and Pinkse (2000), Fiva et al. (2006), Solé-Ollé (2006). The main advantage of using 2SLS instead of ML is that, even in the presence of spatial errors dependence, the estimated coe¢cients remain consistent.²⁴ Moreover, given the set-up of the model, …nding relevant instruments is not too di¢cult. Indeed, as all the communes are considered as setting their tax rate in a perfectly identical way, the most straightforward set of instruments to use is the weighted average of neighbor population characteristics.

Before starting our analysis of the results, various tests were made. First, according to the Shea’s partialR-squared, the instruments we used for the weighted average of neighbor tax rates are not weak. Second, we could not reject the null that the instruments are uncorrelated with the error term and correctly excluded from the 2^nd stage equation.²⁵ Third, to assert the utility of instrumenting for neighbor tax multipliers, we computed a Hausman test²⁶ and we could not reject the null that OLS yield consistent estimates, i.e.

endogeneity among the regressors has no deleterious e¤ect on OLS estimates. Given this result, OLS and 2SLS are both consistent but OLS should be more e¢cient.²⁷ Finally, the overall …t of our OLS estimation is very good since theR-squared is59%.

2 3Using a10km or a20km threshold does not change the results signi…cantly.

2 4See Kelejian and Prucha (1998) for a formal proof of this argument.

2 5The HansenJstatistic reports a value of11:231which does not allow us to rejectH0 (excluded instru-ments are valid instruinstru-ments).

2 6UnderH0: b_OLS andb_2SLS are both consistent butb_OLS is more e¢cient, the Hausman test is given by: (b_2SLS b_OLS)⁰[var(b_2SLS) var(b_OLS)](b_2SLS b_OLS)!^{d 2}_mwheremis the number of instrumented variables.

2 7We also tested for the possible endogeneity of communal population characteristics and we were never able to reject the null of exogeneity.

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Table 4.2: Tax setting and tax base estimations

Model without relocation Strategic interactions model

M-R mod. Benchmark Tax rate (reduced form) Tax rate (structural form) Tax base (structural form)

[1] OLS [2] OLS [3] OLS [4] 2SLS [5] OLS [6] 2SLS [7] 3SLS^a [8] OLS [9] 2SLS [10] 3SLS^a Med./mean income -7.404

[0.49]

Tax -36.780*** -37.214*** -67.495***

[5.55] [3.94] [7.13]

Neighbor tax 0.922*** 0.942*** 0.550*** 0.696*** 0.546*** -55.066*** -54.653*** -24.406**

[8.76] [8.51] [5.67] [5.10] [4.44] [8.18] [4.14] [2.20]

Tax base -0.005*** -0.003* -0.004**

[6.31] [1.85] [2.30]

Age67 -7.142 -2.172 8.574 8.804 -6.95 1.453 11.589

[0.24] [0.08] [0.33] [0.34] [0.29] [0.06] [0.54]

7<age615 69.330** 58.158** 49.306* 49.117** 38.295 43.391* 29.813

[2.19] [2.03] [1.93] [1.98] [1.60] [1.84] [1.60]

Age>65 0.625 -1.462 -33.629* -34.314** -46.035*** -40.607** -15.628

[0.02] [0.08] [1.87] [1.97] [2.84] [2.39] [1.08]

Foreigner -59.035*** -43.246*** 2.811 3.793 13.916 9.538 -4.41

[3.98] [2.82] [0.21] [0.29] [1.16] [0.74] [0.44]

Primary 47.830*** 37.785*** 35.810*** 35.767*** 24.814*** 30.076*** 25.450***

[4.54] [3.68] [4.16] [4.28] [3.32] [3.53] [3.38]

Public 59.210*** 48.190** 29.338 28.936 36.861** 32.799* 18.82

[3.04] [2.44] [1.55] [1.56] [2.09] [1.84] [1.52]

Unemployed 81.150* 75.846 40.475 39.721 26.609 33.134 25.395

[1.66] [1.55] [0.93] [0.94] [0.70] [0.86] [0.85]

Owner -47.859*** -40.403*** -24.899*** -24.568*** -4.097 -12.14 -24.356***

[6.41] [5.41] [3.51] [3.49] [0.60] [1.36] [2.92]

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[1] OLS [2] OLS [3] OLS [4] 2SLS [5] OLS [6] 2SLS [7] 3SLS^a [8] OLS [9] 2SLS [10] 3SLS^a

Density 0.310** 0.365*** 0.379*** 0.379*** 0.394*** 0.368*** 0.287*** -10.082 -9.87 6.353

[2.52] [3.06] [3.52] [3.62] [4.09] [3.84] [2.72] [1.47] [1.33] [0.65]

Acreage 0.003*** 0.002** 0.002*** 0.002*** 0.002*** 0.002*** 0.001**

[3.89] [2.42] [3.46] [3.56] [3.22] [3.27] [1.99]

Altitude 0.022*** 0.006 0.013* 0.013** 0.006 0.007 0.009* -0.537* -0.533 -0.295

[3.10] [0.78] [1.93] [2.00] [1.10] [1.30] [1.78] [1.68] [1.57] [0.65]

Industry -0.544 -0.61 -1.370*** -1.386*** -1.535*** -1.482*** -1.421*** -85.022*** -85.517*** -118.526***

[1.15] [1.24] [3.05] [3.14] [4.20] [3.88] [4.17] [4.43] [3.51] [3.89]

Agriculture 0.124*** 0.039 0.042 0.042 0.086** 0.068* 0.073** 2.25 2.259 4.617

[2.68] [0.78] [0.94] [0.96] [2.47] [1.84] [2.03] [0.75] [0.78] [1.46]

Lake -7.023*** -8.595*** -6.727*** -6.687*** -4.670*** -5.335*** -5.725*** -50.273 -53.484 -263.92

[3.47] [3.30] [2.95] [3.02] [3.17] [3.50] [3.17] [0.24] [0.32] [1.44]

R-squared 0.45 0.5 0.59 0.66 0.63

Neighbor control no yes yes yes no no no yes yes yes

Robustt-statistics in brackets, Constants not reported,^ajointly estimated

* signi…cant at 10%; ** signi…cant at 5%, *** signi…cant at 1%

Notes:

Neighbor controls: density, altitude, industry, agriculture, lake

IV for neighbor tax (specif. [4]): neighbor age dummies, foreigner, primary, public, unemployed, owner, acreage Shea’s partial R-squared: 0.8941***

IV for neighbor tax and tax base (specif. [6]): neighbor age dummies, foreigner, primary, public, unemployed, owner, acreage, neighbor controls:

Shea’s partial R-squared: 0.3944*** (neighbor tax) and 0.1085*** (tax base)

IV for tax (specif. [9]): age dummies, foreigner, primary, public, unemployed, owner, acreage Shea’s partial R-squared: 0.1239***

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The estimated coe¢cients of the “reaction function” are reported in columns [3] and [4]

of table 4.2. The result of main interest is that the coe¢cient on the weighted neighbor tax multiplier is signi…cant at a 1% level with an estimated coe¢cient close to 0:9, i.e. an increase [decrease] in the weighted neighbor tax multiplier leads to an almost similar increase [decrease] of the own tax multiplier. This result seems to con…rm that tax interactions are quite high at a municipal level, thus omitting to take them into account may strongly bias the estimations.²⁸

Among the communal characteristics having a signi…cant in‡uence on the tax multiplier, we …nd that the share of young between7and15has a positive impact on the tax multiplier.

This result con…rms that the …nancing of primary schools²⁹ weighs on the budget constraint of the communes and hence compels them to increase their revenues by setting higher taxes.

The share of people over64has surprisingly a negative impact on tax multiplier. Generally, we would expect citizens over 64 to be on average less mobile than the younger and to need more public services such as health care. However, this negative impact could be explained by older people being also more conservative and hence favoring lower taxes at the booths. We also …nd that the share of primary sector workers has a positive impact on tax multipliers. This result is quite in line with the theoretical predictions since primary sector employees are on average less mobile than secondary or tertiary sector employees.

A high owner share in a commune has a signi…cant negative impact on its tax multiplier which could be explained by owner being on average richer and voting more. Relying on the median voter theorem, a high share of foreigners - without voting rights and earning low incomes - should decrease the level of taxes. In the case of Switzerland, since the foreigners are on average either very high or very low skilled, their impact on the income distribution is not clear cut which may explain that the foreigners share has no signi…cant in‡uence on the communal tax multipliers.

What about geographical characteristics? First, the higher the communal density and size, the higher the tax rate. The result associated with density is not surprising as the communes with a high density are mostly urban and have proportionally more to spend for social security, culture and infrastructure than the communes with a low density. Second, the communes lying at the side of a lake set signi…cantly lower taxes than the other. The lake dummy may capture some unobservable feature such as a high property value - entry barrier - which prevent poorer household to settle in such a commune. Finally, the share of industrial area in a commune has a very signi…cant negative in‡uence on its tax multiplier.

One explanation could rely on the complementarity between the taxes collected: for a given level of communal expenditures, if the corporate income taxes collected are high, the personal income taxes can be set at a lower level.

Contrary to the estimation without strategic interaction presented in column [2], the

2 8For instance, an almost1to1reaction has been found by Brett and Pinkse [?] for municipal tax rates in British Columbia. Fiva et al. [?] have found a coe¢cient of0:8and Revelli [?] of0:6.

2 9As parents have not the choice to which public primary school to send their children, the share of children between7and15is highly correlated with the observed share of primary schoolchildren in a commune.

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neighbor geographical characteristics - not reported - have no signi…cant in‡uence on the tax multiplier set by a commune. This result informs us that neighbor geographical char-acteristics only have an indirect e¤ect - through neighbor taxes - on the own tax multiplier.

Even if these “reaction function” estimations give some very interesting insights on the determinants of the tax rates and on the size of strategic interactions, no information on the channels through which tax interactions occur can be extracted from them. A positive could re‡ect either tax competition for the mobile tax base, or public spillover, or a tax mimicking behavior of communes. To get a further intuition about the underlying determinant of tax interactions, the coe¢cient should be split into two components as follows:

=1+2 (4.7)

where 1 is the direct e¤ect of neighbor tax rates on own tax rates - such as for instance tax mimicking or spillover e¤ects³⁰ - and 2 is an indirect e¤ect possibly associated with a tax base e¤ect as emphasized in the theoretical part.

4.4.4 Estimation of the “structural form” of the tax setting equation